EDA Red Wine quality
Data set introduce
数据的具体情况如下：
## [1] "X" "fixed.acidity" "volatile.acidity"
## [4] "citric.acid" "residual.sugar" "chlorides"
## [7] "free.sulfur.dioxide" "total.sulfur.dioxide" "density"
## [10] "pH" "sulphates" "alcohol"
## [13] "quality"## 'data.frame': 1599 obs. of 13 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ fixed.acidity : num 7.4 7.8 7.8 11.2 7.4 7.4 7.9 7.3 7.8 7.5 ...
## $ volatile.acidity : num 0.7 0.88 0.76 0.28 0.7 0.66 0.6 0.65 0.58 0.5 ...
## $ citric.acid : num 0 0 0.04 0.56 0 0 0.06 0 0.02 0.36 ...
## $ residual.sugar : num 1.9 2.6 2.3 1.9 1.9 1.8 1.6 1.2 2 6.1 ...
## $ chlorides : num 0.076 0.098 0.092 0.075 0.076 0.075 0.069 0.065 0.073 0.071 ...
## $ free.sulfur.dioxide : num 11 25 15 17 11 13 15 15 9 17 ...
## $ total.sulfur.dioxide: num 34 67 54 60 34 40 59 21 18 102 ...
## $ density : num 0.998 0.997 0.997 0.998 0.998 ...
## $ pH : num 3.51 3.2 3.26 3.16 3.51 3.51 3.3 3.39 3.36 3.35 ...
## $ sulphates : num 0.56 0.68 0.65 0.58 0.56 0.56 0.46 0.47 0.57 0.8 ...
## $ alcohol : num 9.4 9.8 9.8 9.8 9.4 9.4 9.4 10 9.5 10.5 ...
## $ quality : int 5 5 5 6 5 5 5 7 7 5 ...## X fixed.acidity volatile.acidity citric.acid
## Min. : 1.0 Min. : 4.60 Min. :0.1200 Min. :0.000
## 1st Qu.: 400.5 1st Qu.: 7.10 1st Qu.:0.3900 1st Qu.:0.090
## Median : 800.0 Median : 7.90 Median :0.5200 Median :0.260
## Mean : 800.0 Mean : 8.32 Mean :0.5278 Mean :0.271
## 3rd Qu.:1199.5 3rd Qu.: 9.20 3rd Qu.:0.6400 3rd Qu.:0.420
## Max. :1599.0 Max. :15.90 Max. :1.5800 Max. :1.000
## residual.sugar chlorides free.sulfur.dioxide
## Min. : 0.900 Min. :0.01200 Min. : 1.00
## 1st Qu.: 1.900 1st Qu.:0.07000 1st Qu.: 7.00
## Median : 2.200 Median :0.07900 Median :14.00
## Mean : 2.539 Mean :0.08747 Mean :15.87
## 3rd Qu.: 2.600 3rd Qu.:0.09000 3rd Qu.:21.00
## Max. :15.500 Max. :0.61100 Max. :72.00
## total.sulfur.dioxide density pH sulphates
## Min. : 6.00 Min. :0.9901 Min. :2.740 Min. :0.3300
## 1st Qu.: 22.00 1st Qu.:0.9956 1st Qu.:3.210 1st Qu.:0.5500
## Median : 38.00 Median :0.9968 Median :3.310 Median :0.6200
## Mean : 46.47 Mean :0.9967 Mean :3.311 Mean :0.6581
## 3rd Qu.: 62.00 3rd Qu.:0.9978 3rd Qu.:3.400 3rd Qu.:0.7300
## Max. :289.00 Max. :1.0037 Max. :4.010 Max. :2.0000
## alcohol quality
## Min. : 8.40 Min. :3.000
## 1st Qu.: 9.50 1st Qu.:5.000
## Median :10.20 Median :6.000
## Mean :10.42 Mean :5.636
## 3rd Qu.:11.10 3rd Qu.:6.000
## Max. :14.90 Max. :8.000Univariate Plots Section
红酒品质的分布：
##
## 3 4 5 6 7 8
## 10 53 681 638 199 18
从上图可以看到，红酒品质的数据分布并不均匀，主要品质是5和6.
##
## Low_Q Meddle_Q High_Q
## 744 638 217## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 8.40 9.50 10.20 10.42 11.10 14.90
红酒pHz值主要分布在2.8-3.8， 呈酸性。
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.3300 0.5500 0.6200 0.6581 0.7300 2.0000
红酒的特征sulphates数据是长尾分布，取值区间主要为(0.3, 1.2)
红酒的desity呈正太分布.
红酒的特征total.sulfur.dioxide呈长尾分布，主要取值范围在区间（5-80）.
红酒的特征free.sulfur.dioxide呈长尾分布，主要取值范围在区间（0-40）
红酒的特征chlorides呈正态分布，主要取值范围在区间（0.03, 0.14）.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4.60 7.10 7.90 8.32 9.20 15.90红酒的特征fixed.acidity主要取值范围在区间（5, 12), 均值为8.32.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.1200 0.3900 0.5200 0.5278 0.6400 1.5800
红酒的特征volatile.acidity主要取值范围在区间（0.2, 1.0), 均值为0.5278.
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 0.900 1.900 2.200 2.539 2.600 15.500
红酒中糖分留存量（residual sugar）取值在 (1.9, 2.6), 长尾分布。
可以看到有四个取值数特别高：0, 0.02, 0.24,0.49
Univariate Analysis
What is the structure of your dataset?
出去X为索引数，总共1599观察数据，每个数据有11个数值变量，还有一个品质评定的分类的变量，没有无效特征值。
一些特征数据有长尾，如residual.sugar
一些特征数据有红酒的特征呈正态分布，如chlorides，主要取值范围集中区间（0.03, 0.14）
What is/are the main feature(s) of interest in your dataset?
红酒的品质，以及对其影响比较大的特征：sulphates，alcohol和Ph。
What other features in the dataset do you think will help support your investigation into your feature(s) of interest?
比如residual.sugar, , chlorides, density and
Did you create any new variables from existing variables in the dataset?
新增了一个品质等级，相应的总数为：
Low_Q：744
Meddle_Q：638
High_Q：217
Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?
有些数据存在长尾现象，进行相应的规范处理。这样可以让数据图看起来更明了，更容易抓住其中隐藏的信息。
Bivariate Plots Section
ref to How to read a box plot/Introduction to box plots
ggcorr函数整体查看下变量之间的相关性，由上图相互间相关系数可知，对红酒品质的影响可以分：
alcohol和sulphol都是强正相关；
fixed.acidity和citric.acid都是弱正相关；
volatile.acidity强负相关；
chlorides, density弱负相关
当然，有些特征间相关性极高，还可以看到pH与fixed.acidity相关性高，但对品质相关性为0，很十奇怪。
由上图明显看出，酒精度对品质有明显的影响。
density对酒精度有明显的负影响，那它们间的关系有如何呢？
随着浓度的升高，酒精度下降了。
## $x
## [1] "Quality (score between 3 and 9)"
##
## $y
## [1] "volatile.acidity (acetic acid - g/dm^3)"
##
## $title
## [1] "Boxplot of volatile.acidity across Red Wine qualities"
##
## attr(,"class")
## [1] "labels"由上图明显看出，volatile.acidity对品质有明显的负影响。
看上图，pH似乎对品质还是有一点点的影响， 具体的相关系数计算如下为：-0.05773139，其实也并非为0.
## [1] -0.05773139
## [1] 0.2513971看上图，sulphates对品质还是相当的影响， 具体的相关系数： 0.2513971.
citric.acid和volatile.acidity对红酒品质影响十相反的，那相互之间呢？ 
citric.acid与volatile.acidity含量是负相关的。
Bivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?
pH似乎对品质还是有一点点的影响，但很小；
sulphates对品质还是相当高的影响；
citric.acid与volatile.acidity含量是负相关的
Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?
density对酒精度（alcohol）有明显的负影响，随着浓度的升高，酒精度下降了。
What was the strongest relationship you found?
酒精度（alcohol）对红酒品质有非常强的影响
Multivariate Plots Section
上图可知，一般来说，品评好酒需要density／alcohol两个一起看。
上图可分析出，当volatile.acidity／alcohol两个都标注的时候，只需看酒精度就能判断红酒品质高低。
Multivariate Analysis
Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?
品评好酒需要density／alcohol两个一起看。
Were there any interesting or surprising interactions between features?
当volatile.acidity／alcohol两个都标注的时候，只需看酒精度就能判断红酒品质高低。
OPTIONAL: Did you create any models with your dataset? Discuss the strengths and limitations of your model.
##
## Calls:
## m1: lm(formula = quality ~ alcohol, data = training_data)
## m2: lm(formula = quality ~ alcohol + sulphates, data = training_data)
## m3: lm(formula = quality ~ alcohol + sulphates + volatile.acidity,
## data = training_data)
## m4: lm(formula = quality ~ alcohol + sulphates + volatile.acidity +
## chlorides, data = training_data)
## m5: lm(formula = quality ~ alcohol + sulphates + volatile.acidity +
## chlorides + pH, data = training_data)
##
## ==========================================================================================
## m1 m2 m3 m4 m5
## ------------------------------------------------------------------------------------------
## (Intercept) 2.055*** 1.550*** 2.786*** 2.957*** 4.027***
## (0.197) (0.203) (0.217) (0.220) (0.446)
## alcohol 0.344*** 0.336*** 0.303*** 0.285*** 0.297***
## (0.019) (0.018) (0.018) (0.018) (0.019)
## sulphates 0.904*** 0.591*** 0.791*** 0.761***
## (0.113) (0.110) (0.121) (0.121)
## volatile.acidity -1.307*** -1.248*** -1.156***
## (0.107) (0.107) (0.112)
## chlorides -1.725*** -1.969***
## (0.448) (0.456)
## pH -0.363**
## (0.132)
## ------------------------------------------------------------------------------------------
## R-squared 0.208 0.245 0.324 0.332 0.336
## adj. R-squared 0.207 0.244 0.323 0.330 0.334
## sigma 0.718 0.701 0.663 0.659 0.658
## F 334.445 207.298 204.116 158.451 128.933
## p 0.000 0.000 0.000 0.000 0.000
## Log-likelihood -1389.314 -1358.149 -1287.245 -1279.849 -1276.050
## Deviance 657.508 626.234 560.511 554.066 550.784
## AIC 2784.628 2724.299 2584.489 2571.697 2566.099
## BIC 2800.090 2744.914 2610.258 2602.620 2602.176
## N 1279 1279 1279 1279 1279
## ==========================================================================================
我们的模型可以推算误差接近0，但是不同品质的酒预测精度并不一样。quality 5/6明显要高于其他数据组。
Final Plots and Summary
Plot One
Description One
根据红酒的评分，划分了三个等级，相应的分布如上所示，低品质的酒要明显高于高品质，看来买到好酒不容易。
Plot Two
Description Two
由上图明显看出，酒精度对品质有明显的影响。所以，买酒先看酒精度数。
Plot Three
Description Three
density／alcohol都对红酒的品质有明显的影响。
Reflection
- 通过本次作业，熟练R相关的操作，特别ggplot，相关作图非常清晰，简单。虽然与python语法很大不同，但操作更简单。
- 分析模型那部分可看到，数据少的组，得出的错误率明显要高，怎么提高模型的精度是下一步可以进行的学习。
- 如何分析更多，不那么整洁的数据，还需要更多的练习。